Proposition 3 (Biclique Partition and Chromatic Number [1]}) 

For any \(n \in \mathbb {N}\) , there exists a simple graph \(G\)  with
\(\mathrm {bp}(G) = n\)  such that
\(\chi (G) \ge n^{(\log (n))^{1-\epsilon (n)}}\,,\) 
